Abstract
The ultrafilter semigroup of a topological group G, denoted Ult(G), consists of all nonprincipal ultrafilters on G converging to the identity and is a closed subsemigroup in the Stone-Cech compactification β Gd of G as a discrete semigroup. We show that for every countable nondiscrete Abelian topological group G not containing an open Boolean subgroup, the structural group of the smallest ideal of Ult(G) has cardinality 2c.
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